Abstract
ABSTRACTWe study the almost sure convergence of integrated square error of the wavelet density estimators for multivariate absolutely regular observations. We state that these estimates reach, up to a logarithm, the optimal rate of -almost sure convergence for densities in the Sobolev space with s > 0. The support of f may be the whole space . Precisely, if fn is a such estimate of f, we prove that , a.s. Moreover, we give an estimate of the constant in this upper bound. Proofs are based on Hilbertian approach and Bernstein type inequalities for dependent Hilbertian random vectors.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have